We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the reconstruction is a semantic representation from which the source can be probabilistically generated, rather than a pointwise approximation. We formulate the corresponding rate-distortion problem and characterize fundamental properties of the resulting rate-distortion function, including its connections to lossy compression under log-loss, classical rate-distortion problems with arbitrary distortion measures, and rate-distortion with perfect perception.

翻译：本文研究在由预设条件分布$P_{X|U}$诱导的负对数似然所定义的失真度量下的有损信源编码问题。这种对数似然失真建模的压缩场景中，重构结果是一种能够以概率方式生成源信号的语义表示，而非逐点近似。我们建立了相应的率失真问题框架，并刻画了所得率失真函数的基本性质，包括其与对数损失下有损压缩、采用任意失真度量的经典率失真问题、以及具有完美感知约束的率失真理论之间的内在联系。